Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $\lim\limits_{x\to a^+} f(x)=L$ and if $c$ is a function such that $a < c(x) < x$ for all $x > a$, then $\lim\limits_{x\to a^+} f(c(x))=L$. Note: there has been no discussion about continuity or any discussion about the limits of composition functions at this point. Any help would be appreciated!

share|cite|improve this question
For some basic information about writing math at this site see e.g. here, here, here and here. – Martin Sleziak Oct 10 '12 at 12:19
up vote 1 down vote accepted

Let $\epsilon>0$. Then there exists a $\delta>0$ such that

$|f(x)-L|<\epsilon$ whenever $0<x-a<\delta$. Notice that, $0<c(x)-a<x-a<\delta$, so that in particular, $0<c(x)-a<\delta$ and hence:


share|cite|improve this answer
I was definitely over-analyzing the problem. Your explanation makes a lot of sense.Thanks – user42864 Oct 10 '12 at 0:30

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.